The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model)

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The study is about impact of a short elastic rod(or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. In the process of predicting the stress and velocity of wave propagation using viscoelastic discontinuity, the Z-effective which is the effective ratio of acoustic impedance plays important role. It can be shown that effective ratio of acoustic impedance can help us to determine whether the slug and the rod move together or part company after the impact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

Original languageEnglish
Title of host publicationInternational Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013
Pages146-151
Number of pages6
DOIs
Publication statusPublished - 11 Nov 2013
EventInternational Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Kuala Lumpur, Malaysia
Duration: 05 Feb 201307 Feb 2013

Publication series

NameAIP Conference Proceedings
Volume1557
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013
CountryMalaysia
CityKuala Lumpur
Period05/02/1307/02/13

Fingerprint

acoustic impedance
wave propagation
rods
discontinuity
Laplace equation
partial differential equations
compatibility
time constant
impulses
poles
viscosity
inversions
boundary conditions
momentum

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Haji Musa, A. B. (2013). The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model). In International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013 (pp. 146-151). (AIP Conference Proceedings; Vol. 1557). https://doi.org/10.1063/1.4823893
Haji Musa, Abu Bakar. / The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model). International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. 2013. pp. 146-151 (AIP Conference Proceedings).
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Haji Musa, AB 2013, The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model). in International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP Conference Proceedings, vol. 1557, pp. 146-151, International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013, Kuala Lumpur, Malaysia, 05/02/13. https://doi.org/10.1063/1.4823893

The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model). / Haji Musa, Abu Bakar.

International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. 2013. p. 146-151 (AIP Conference Proceedings; Vol. 1557).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - The study is about impact of a short elastic rod(or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. In the process of predicting the stress and velocity of wave propagation using viscoelastic discontinuity, the Z-effective which is the effective ratio of acoustic impedance plays important role. It can be shown that effective ratio of acoustic impedance can help us to determine whether the slug and the rod move together or part company after the impact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

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Haji Musa AB. The effective ratio of acoustic impedance in predicting stress and velocity of wave propagation in viscoelastic material (standard linear solid model). In International Conference on Mathematical Sciences and Statistics 2013, ICMSS 2013 - Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. 2013. p. 146-151. (AIP Conference Proceedings). https://doi.org/10.1063/1.4823893